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Simplifying 18y2 + -1y + -1 = 0 Reorder the terms: -1 + -1y + 18y2 = 0 Solving -1 + -1y + 18y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + -0.05555555556y + y2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + -0.05555555556y + 0.05555555556 + y2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + -0.05555555556y + y2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + -0.05555555556y + y2 = 0 + 0.05555555556 -0.05555555556y + y2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 -0.05555555556y + y2 = 0.05555555556 The y term is -0.05555555556y. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556y + 0.0007716049384 + y2 = 0.05555555556 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556y + y2 = 0.05555555556 + 0.0007716049384 Combine like terms: 0.05555555556 + 0.0007716049384 = 0.0563271604984 0.0007716049384 + -0.05555555556y + y2 = 0.0563271604984 Factor a perfect square on the left side: (y + -0.02777777778)(y + -0.02777777778) = 0.0563271604984 Calculate the square root of the right side: 0.237333437 Break this problem into two subproblems by setting (y + -0.02777777778) equal to 0.237333437 and -0.237333437.Subproblem 1
y + -0.02777777778 = 0.237333437 Simplifying y + -0.02777777778 = 0.237333437 Reorder the terms: -0.02777777778 + y = 0.237333437 Solving -0.02777777778 + y = 0.237333437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + y = 0.237333437 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + y = 0.237333437 + 0.02777777778 y = 0.237333437 + 0.02777777778 Combine like terms: 0.237333437 + 0.02777777778 = 0.26511121478 y = 0.26511121478 Simplifying y = 0.26511121478Subproblem 2
y + -0.02777777778 = -0.237333437 Simplifying y + -0.02777777778 = -0.237333437 Reorder the terms: -0.02777777778 + y = -0.237333437 Solving -0.02777777778 + y = -0.237333437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + y = -0.237333437 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + y = -0.237333437 + 0.02777777778 y = -0.237333437 + 0.02777777778 Combine like terms: -0.237333437 + 0.02777777778 = -0.20955565922 y = -0.20955565922 Simplifying y = -0.20955565922Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.26511121478, -0.20955565922}
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